- List of equations in classical mechanics
physicsused to describe the motion of macroscopicobjects. [Harvnb|Mayer|Sussman|Wisdom|2001|p=xiii] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [Harvnb|Berkshire|Kibble|2004|p=1] The subject is based upon a three-dimensional Euclidean spacewith fixed axes, called a frame of reference. The point of concurrency of the three axes is known as the origin of the particular space. [Harvnb|Berkshire|Kibble|2004|p=2]
Classical mechanics utilises many
equation—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equationss, manifolds, Lie groups, and ergodic theory. [Harvnb|Arnold|1989|p=v] This page gives a summary of the most important of these.
: ("R" = radius of the circle, ω = "v/R"
angular velocity) Momentum
: (Constant Mass)
::if F is constant
Moment of inertia
For a single
axis of rotation:The moment of inertia for an object is the sum of the products of the mass element and the square of their distances from the axis of rotation: Angular momentum
: if v is perpendicular to r
(Note: I can be treated like a vector if it is diagonalized first, but it is actually a 3×3 matrix - a
r is the radius vector.
::if |r| and the sine of the angle between r and p remains constant.:This one is very limited, more added later. α = dω/dt
Omega is called the precession angular speed, and is defined:
(Note: w is the weight of the spinning flywheel)
for "m" as a constant:
: in field of gravity
Central force motion
Equations of motion(constant acceleration)
These equations can be used only when acceleration is constant. If acceleration is not constant then
calculusmust be used.
Derivation of these equation in vector format and without having is shown here These equations can be adapted for angular motion, where angular acceleration is constant:
*citation|title=Mathematical Methods of Classical Mechanics|last=Arnold|first=Vladimir I.|publisher=Springer|year=1989|isbn=978-0-387-96890-2|edition=2nd
*citation|title=Classical Mechanics|last1=Berkshire|last2=Kibble|first1=Frank H.|first2=T. W. B.|edition=5th|publisher=Imperial College Press|year=2004|isbn=978-1860944352
*citation|title=Structure and Interpretation of Classical Mechanics|last1=Mayer|last2=Sussman|last3=Wisdom|first1=Meinhard E.|first2=Gerard J.|first3=Jack|publisher=MIT Press|year=2001|isbn=978-0262194556
* [http://www.astro.uvic.ca/~tatum/classmechs.html Lectures on classical mechanics]
* [http://scienceworld.wolfram.com/biography/Newton.html Biography of Isaac Newton, a key contributor to classical mechanics]
Classical mechanics is the branch of
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